Remember that after the assassination that Angleton essentially turned the counter intelligence division upside down due to his insistence that Nosenko was a fake agent sent by the KGB to cover up their supposed connections to Oswald. And any possible role in the assassination. Nosenko was brutally treated on Angleton's orders in an attempt to get him to confess.
If Angleton was behind the assassination - and thus Oswald was innocent of the murder and any KGB connection meaningless to the event - why do all of that? It serves no purpose. Why turn CI into a operational mess over something he knew wasn't true? I.e., that the KGB had a role in the assassination. They didn't. Angleton essentially destroyed his career due to the mistreatment of Nosenko. Yes, the other stuff - the mail openings - contributed to it. It doesn't make sense to me.
Who knows? James Angleton's paranoia (post the Philby incident) is well documented.
If he had any involvement with JFK's assassination (even indirectly), it was in his interest to point the finger at the Soviets.
Any luck finding that Morley quote that you referenced earlier?
Somewhat off-topic but still on the topic of conspiracies, the Trump-Russia collusion theory is a recent conspiracy that many people on the Left in the US have speculated about. I too initially thought the theory had legs but over time, the more I learned about the Trump-Russia investigations, the less I believed it to be probable that there was any sort of agreement or conspiracy between Trump and Putin.
The Kennedy assassination for me has been the opposite. The more I've learned, the more I've leaned towards the conclusion that there probably was a conspiracy.